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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 325r

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.83.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 326v); this page is its right half.

The machine reads it as

  1. 1 septemtur 9s.
  2. dy = 10 + 1y + 12 y+ 139+ 14 yt ete :20 +21y+ 22y + 9 y + 24y ek
  3. (2)
  4. 30 + 319 4 32 1 +33y + 34 st Betc. 20 fit d, L 30 + yd31 + yd3r + 9 d33 + g 3 F 131 229 1ii
  5. fit (10. in 1. 31 + 2. 329 + 3,33y 4 4. 341+5. 35y + 6. 36y3 + 7 27 y etc
  6. 1. 31 232 3.33 4.34 5. 35 6. 36
  7. 1.31 2.32 3. 33. 4.34. 5.35
  8. 1.31 2. 32 3.33 4. 34
  9. etc et etc
  10. 20 n d3o du. dir d33. d3+ d35 d36
  11. deo, dyt d32
  12. d33 d34 d35
  13. d3.0 d31 d32 d33 d34
  14. d30, d31 d32 433
  15. et et et
  16. Haec oq. 4. debet esseidenci
  17. cum aeq. 2. Et cum aeg. 2
  18. ponatur esse formula ratio
  19. naliter in divisibilis
  20. sequitur multiplicitam
  21. per arbitrariam coincidere
  22. eum ipsa 5q. 4.
  23. Multiplicata ergo aq. 2. per formalam generatem 40 + 41y+ +2y +3 es
  24. dabit:
  25. eo 4 1o
  26. 30. 40 + 30 41 y + V. 42) + 30. 1G G. + 2. 44y 4 30. 4519 +30461
  27. +31.40 31.41 31ge 31. 43 31. 44 31.45
  28. 32.40 32. 91 31. 42 92. 49 3244
  29. 33.40 33. 41 33. 4e 33. B
  30. Et coincident aeq. J. et
  31. per nihil omniuo, deinde quototum
  32. et et etc
  33. Et examinemus primo casum quo multiplicatur aeq. 2. solum per 40. deinde
  34. quo per 40+41y, deinde cusem ubi per 41 +427 + 431, et ta porro
  35. quetalibet horum casuum, ducamus per casum quo differentiae primae
  36. ipsarum 30, 31, 42 etc. sunt constantes, seu quo secundae differentiae comnescunt
  37. Inde pergamus sunt aequales nihilo, inde pergamas ad casum quo secunde
  38. tertiae sunt aequales nihito, inde ad casum quo quartae. Ita casus ubi scundae
  39. evartescunt, potest intelligi comprehensus in ex quo tertiae evanescuntu, et ita
  40. si per nihil omnino multiplicetur 8g. 2, debebunt comparari
  41. aequatio 2 et 4. Et sint primum, omnes termini 30, 31, 32, 33 et
  42. R
  43. aauatua at
  44. porro. P.
  45. Higus fit 30 = 10. 1. 31 + 20. 50j Ergo 307 = 10. 1. 3H F 101. 1.39 ( 20. 3091 201301
  46. deceu
  47. un
  48. Ad observandam in calculo legem homogeneorum res ad numeros revocetur, et quidem
  49. 10, 2, 40 sunt dimensionis o d d3, vel d3t, et suibatur 301, s 3II; et sunliter
  50. et dd3o vel dd31 scribatur 302, 312. et ddd3o vel ddd31 sctibatur 303, 313, etc.
  51. 11, 21 etc. dimensionis - 1 12, 22 dimensionis - 1. et,
  52. 3, Rro, et suit dimersionis e, erit 3
  53. 101, 201, 301, etc. dimensionis - 1. et 111, 211 es dimensionis -2, et 121, 221, 327, etc. dimensionis - 3
  54. 10, 20, 30 sint dimensionis 0,
  55. et 102, 202,302, et C. dimensionis - 1 et 112, 212, 312 e d mensonis 3 et 122, 222, 322, etc dimensionis -4, et
  56. Hinc sequitur ut comparari possint aegg. 2 et 4. salva ege homogeneorum, debere mmultiplicari
  57. aqu. 3b. saltem per 41 vel 42y etc. Et Ret 20. 41 + 3141y + 32. 4115 etc=0 comparanda
  58. cum aeq. 4. ita fiet 30. 21= 10. 1. 31 + 20. 301, ubi servatur lex homogenectum, nam ubique summa
  59. Et diffeatiano fit Caecterum sponatur revera aeq2 non fuisse
  60. multiplicata nrisi per contantem; sumemus 4l. pro qconstante quasi valeret 1: a, seu a. et
  61. characterum, (non cputatis primis) est 1
  62. 301. 4) = 16. 1. 311 + 101. 1. 314 20. 302 + 201. 30)
  63. uinque 10 sit data, si 101 non est acoportet esse 31 constantem, ex contra
  64. ihil variabid. Et ex aey. 3. differentiando1 Alco
  65. E1.41 L10. 2. 32 +11. 1. 31 + 20. 311 + 21. 301.
  66. 301. H. 4
  67. 101. 311. 4
  68. a
  69. (10 i 32 toll a ngur +. 20, 311. (041 4 21, 301. 1ol1
  70. te
  71. H. 11.1
  72. =101. 311. I1. 1
  73. Eot hor ut
  74. vadto tamen si VI Lo si 10 constans fit 311 = 201. d
  75. 10. 1
  76. in 31 constans sil 31, = 301. 41 - 201. 301, : 101. 1
  77. Asi ergo 31 fitostans, et 32 - 8. fiet 30C fvanescet 301, et fiet 41. 41 701. 41 = 41. 11. 1 - 201. 11. 1 f 21 41,
  78. seu fic a1- 201. H M a Y
  79. I1.
  80. L

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 325r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0645?run=74